Line formation in convective stellar atmospheres. I. Granulation corrections for solar photospheric abundances

In an effort to estimate the largely unknown effects of photospheric temperature fluctuations on spectroscopic abundance determinations, we have studied the problem of LTE line formation in the inhomogeneous solar photosphere based on detailed 2-dimensional radiation hydrodynamics simulations of the convective surface layers of the Sun. By means of a strictly differential 1D/2D comparison of the emergent equivalent widths, we have derived ``granulation abundance corrections'' for individual lines, which have to be applied to standard abundance determinations based on homogeneous 1D model atmospheres in order to correct for the influence of the photospheric temperature fluctuations. In general, we find a line strengthening in the presence of temperature inhomogeneities as a consequence of the non-linear temperature dependence of the line opacity. The resulting corrections are negligible for lines with an excitation potential around E_i=5 eV, regardless of element and ionization stage. Moderate granulation effects (Delta_gran ~ -0.1 dex) are obtained for weak, high-excitation lines (E_i >~ 10 eV) of C I, N I, O I as well as Mg II and Si II. The largest corrections are found for ground state lines (E_i=0 eV) of neutral atoms with an ionization potential between 6 and 8 eV like Mg I, Ca I, Ti I, Fe I, amounting to Delta_gran ~ -0.3 dex in the case of Ti I. For many lines of practical relevance, the magnitude of the abundance correction may be estimated from interpolation in the tables and graphs provided with this paper. The application of abundance corrections may often be an acceptable alternative to a detailed fitting of individual line profiles based on hydrodynamical simulations. The present study should be helpful in providing upper bounds for possible errors of spectroscopic abundance analyses, and for identifying spectral lines which are least sensitive to the influence of photospheric temperature inhomogeneities.